{"id":"https://openalex.org/W4410136482","doi":"https://doi.org/10.1007/s40314-025-03219-6","title":"Efficient solution of one-dimensional time-dependent partial differential equations using a multi-step block method combined with compact finite difference schemes","display_name":"Efficient solution of one-dimensional time-dependent partial differential equations using a multi-step block method combined with compact finite difference schemes","publication_year":2025,"publication_date":"2025-05-06","ids":{"openalex":"https://openalex.org/W4410136482","doi":"https://doi.org/10.1007/s40314-025-03219-6"},"language":"en","primary_location":{"id":"doi:10.1007/s40314-025-03219-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40314-025-03219-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40314-025-03219-6.pdf","source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["1807-0302","2238-3603"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s40314-025-03219-6.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087383578","display_name":"Akansha Mehta","orcid":"https://orcid.org/0009-0009-0476-6816"},"institutions":[{"id":"https://openalex.org/I94616015","display_name":"Punjab Technical University","ror":"https://ror.org/025kz2973","country_code":"IN","type":"education","lineage":["https://openalex.org/I94616015"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Akansha Mehta","raw_affiliation_strings":["Department of Mathematics, I. K. Gujral Punjab Technical University, Main Campus, Kapurthala, Jalandhar, Punjab, 144603, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, I. K. Gujral Punjab Technical University, Main Campus, Kapurthala, Jalandhar, Punjab, 144603, India","institution_ids":["https://openalex.org/I94616015"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055161545","display_name":"Gurjinder Singh","orcid":"https://orcid.org/0000-0001-9708-8608"},"institutions":[{"id":"https://openalex.org/I94616015","display_name":"Punjab Technical University","ror":"https://ror.org/025kz2973","country_code":"IN","type":"education","lineage":["https://openalex.org/I94616015"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Gurjinder Singh","raw_affiliation_strings":["Department of Mathematics, I. K. Gujral Punjab Technical University, Main Campus, Kapurthala, Jalandhar, Punjab, 144603, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, I. K. Gujral Punjab Technical University, Main Campus, Kapurthala, Jalandhar, Punjab, 144603, India","institution_ids":["https://openalex.org/I94616015"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005180650","display_name":"Higinio Ramos","orcid":"https://orcid.org/0000-0003-2791-6230"},"institutions":[{"id":"https://openalex.org/I184999862","display_name":"Universidad de Salamanca","ror":"https://ror.org/02f40zc51","country_code":"ES","type":"education","lineage":["https://openalex.org/I184999862"]},{"id":"https://openalex.org/I4210128281","display_name":"Hospital Virgen de la Concha","ror":"https://ror.org/02bhk3j29","country_code":"ES","type":"healthcare","lineage":["https://openalex.org/I4210128281"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Higinio Ramos","raw_affiliation_strings":["Escuela Polit\u00e9cnica Superior de Zamora, Campus Viriato, 49022, Zamora, Spain","Scientific Computing Group, Universidad de Salamanca, Plaza de la Merced, 37008, Salamanca, Spain"],"affiliations":[{"raw_affiliation_string":"Escuela Polit\u00e9cnica Superior de Zamora, Campus Viriato, 49022, Zamora, Spain","institution_ids":["https://openalex.org/I4210128281"]},{"raw_affiliation_string":"Scientific Computing Group, Universidad de Salamanca, Plaza de la Merced, 37008, Salamanca, Spain","institution_ids":["https://openalex.org/I184999862"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5087383578"],"corresponding_institution_ids":["https://openalex.org/I94616015"],"apc_list":null,"apc_paid":null,"fwci":5.7109,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.95352915,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"44","issue":"5","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.6349941492080688},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5734050273895264},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5597796440124512},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5306738018989563},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.4976702034473419},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.4693962633609772},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3562924563884735},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34211355447769165},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33879202604293823},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09141704440116882}],"concepts":[{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.6349941492080688},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5734050273895264},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5597796440124512},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5306738018989563},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.4976702034473419},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.4693962633609772},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3562924563884735},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34211355447769165},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33879202604293823},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09141704440116882}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s40314-025-03219-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40314-025-03219-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40314-025-03219-6.pdf","source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["1807-0302","2238-3603"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s40314-025-03219-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40314-025-03219-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40314-025-03219-6.pdf","source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["1807-0302","2238-3603"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320328269","display_name":"Universidad de Salamanca","ror":"https://ror.org/02f40zc51"},{"id":"https://openalex.org/F4320328351","display_name":"Junta de Castilla y Le\u00f3n","ror":"https://ror.org/02s8dab97"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4410136482.pdf","grobid_xml":"https://content.openalex.org/works/W4410136482.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W626545488","https://openalex.org/W1587859748","https://openalex.org/W1970735434","https://openalex.org/W1972843771","https://openalex.org/W1994391441","https://openalex.org/W1995504856","https://openalex.org/W2047993099","https://openalex.org/W2072655566","https://openalex.org/W2075621314","https://openalex.org/W2077221255","https://openalex.org/W2085481725","https://openalex.org/W2103606462","https://openalex.org/W2610629502","https://openalex.org/W2789416028","https://openalex.org/W2901359631","https://openalex.org/W2912700048","https://openalex.org/W2916722737","https://openalex.org/W3022597404","https://openalex.org/W3164729664","https://openalex.org/W3217717718","https://openalex.org/W4206726559","https://openalex.org/W4230278521","https://openalex.org/W4280552307","https://openalex.org/W4296285787","https://openalex.org/W4300831640"],"related_works":["https://openalex.org/W2330640442","https://openalex.org/W1544816068","https://openalex.org/W1975234065","https://openalex.org/W2171402820","https://openalex.org/W4251142058","https://openalex.org/W2392533133","https://openalex.org/W2617981106","https://openalex.org/W1965041963","https://openalex.org/W2007426143","https://openalex.org/W2384221708"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2,140,199],"paper,":[3],"an":[4],"$$\\mathcal":[5],"{A}$$":[6],"<mml:math":[7],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[8],"<mml:mi>A</mml:mi>":[9],"</mml:math>":[10],"-stable":[11],"four-step":[12],"block":[13,65],"method":[14,66],"of":[15,26,35,59,85,95,102,115,122,150],"order":[16,60],"seven":[17],"has":[18,144,181],"been":[19,69],"developed":[20,64],"to":[21,71,111,184,207],"numerically":[22],"approximate":[23],"the":[24,33,48,63,73,76,86,96,113,116,123,129,151,165,177,190,212],"solution":[25,74],"first-order":[27,36],"ordinary":[28],"differential":[29,41],"equations":[30,42],"obtained":[31],"through":[32],"semi-discretization":[34],"time-dependent":[37],"physically":[38],"relevant":[39],"partial":[40],"(PDEs).":[43],"The":[44,79,92,172],"spatial-derivatives":[45],"involved":[46],"in":[47,75,81,211],"PDE":[49],"are":[50],"discretized":[51],"utilizing":[52],"conventional":[53],"compact":[54],"finite":[55],"difference":[56],"schemes":[57],"(CFDS)":[58],"four,":[61],"and":[62],"is":[67,89,106,136],"then":[68],"implemented":[70],"advance":[72],"time":[77],"direction.":[78],"implementation":[80,175],"variable":[82,173],"step-size":[83,174,192],"mode":[84],"proposed":[87,117],"strategy":[88],"also":[90],"discussed.":[91],"generalized":[93,124],"form":[94],"Burgers-Huxley":[97,125],"equation,":[98,126],"along":[99],"with":[100,168],"some":[101,208],"its":[103],"special":[104,120],"cases,":[105],"examined":[107],"as":[108,128,158,160],"benchmark":[109],"problems":[110,180],"demonstrate":[112],"efficacy":[114],"strategy.":[118],"A":[119],"case":[121,149,163],"known":[127],"Chafee-Infante":[130],"problem,":[131],"involving":[132,164],"Neumann":[133],"boundary":[134],"conditions,":[135],"solved":[137,146],"accurately":[138],"using":[139],"approach.":[141,193],"Additionally,":[142],"it":[143],"efficiently":[145],"a":[147,161,202],"challenging":[148],"Burgers\u2019":[152],"equation":[153,167],"for":[154],"small":[155],"viscosity":[156],"coefficients,":[157],"well":[159],"complex":[162],"FitzHugh-Nagumo":[166],"stiff":[169],"parameter":[170],"values.":[171],"on":[176],"considered":[178],"test":[179],"turned":[182],"out":[183],"be":[185,196],"more":[186],"computationally":[187],"efficient":[188,204],"than":[189],"fixed":[191],"It":[194],"can":[195],"observed":[197],"that":[198],"approach":[200],"provides":[201],"very":[203],"algorithm":[205],"compared":[206],"existing":[209],"techniques":[210],"literature.":[213]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}
